(1) No one will take any company seriously that has their Web site hosted by one of the free Web page hosts. It doesn't say a lot for a company that can't even afford to pay for their own Web space.
(2) You will have a domain name that is relevant to your company and is much easier to remember for future reference. Let's say my domain name is "yahoo.com". Now imagine that it is "freespacehost.com/uk/business/yahoo". Which one is easier to remember?

What makes a good domain name?
The name of your company is always a good choice. If your company name is rather long and hard to remember, then choose something easy to remember and associates with your product or service.

What characters can I use in my domain name and how long can it be?
A web address can have up to 26 characters (including the four characters in .com, .net or .org). You may use any combination of letters and numbers, as well as a "dash" (-), as long as you do not begin or end your name with a dash. No special characters (@&(*^$#) are allowed.
Please note that there is no need to begin your domain name with "www.".

The different types of domains:

.com
.com is for commercial organizations.

.net
.net is for entities and computers that represent part of the Internet's infrastructure.

.org
.org is for miscellaneous entities that do not fit under any of the other top level domains; typically used for nonprofit organizations.

.edu
.edu is for four-year, degree-granting colleges and universities.

.gov
.gov is for agencies and branches of the United States Federal Government.

.mil
.mil is for branchs of the the United States Military.